Global Navigation Satellite Systems (GNSS) include the Global Positioning System (GPS), the Glonass system, and the proposed Galileo system. Each GPS satellite transmits continuously using two radio frequencies in the L-band, referred to as L1 and L2, at respective frequencies of 1575.41 MHz and 1227.60 MHz. Two signals are transmitted on L1, one for civil users and the other for users authorized by the Unites States Department of Defense (DoD). One signal is transmitted on L2, intended only for DoD-authorized users. Each GPS signal has a carrier at the L1 and L2 frequency, a pseudo-random number (PRN) code, and satellite navigation data. Two different PRN codes are transmitted by each satellite: a coarse acquisition (C/A) code and a precision (P/Y) code which is encrypted for DoD-authorized users. Each C/A code is a unique sequence of 1023 bits, which is repeated each millisecond.
FIG. 1 schematically illustrates a typical prior-art scenario to determine the position of a mobile receiver (rover). Rover 100 receives GPS signals from any number of satellites in view, such as SV1, SV2, and SVM, shown respectively at 110, 120 and 130. The signals pass through the earth's ionosphere 140 and through the earth's troposphere 150. Each signal has two frequencies, L1 and L2. Receiver 100 determines from the signals respective pseudo-ranges, PR1, PR2, . . . , PRM, to each of the satellites. Pseudo-range determinations are distorted by variations in the signal paths which result from passage of the signals through the ionosphere and the troposphere, and from multipath effects, as indicated schematically at 160.
Pseudo-range can be determined using the C/A code with an error of about one meter, a civil receiver not using the military-only P/Y code determines rover position with an error in the range of meters. However, the phases of the L1 and L2 carriers can be measured with an accuracy of 0.01-0.05 cycles (corresponding to pseudo-range errors of 2 mm to 1 cm), allowing relative position of the rover to be estimated with errors in the range of millimeters to centimeters. Accurately measuring the phase of the L1 and L2 carriers requires a good knowledge of the effect of the ionosphere and the troposphere for all observation times.
The largest error in carrier-phase positioning solutions is introduced by the ionosphere, a layer of charged gases surrounding the earth. When the signals radiated from the satellites penetrate this medium on their way to the ground-based receivers, they experience delays in their signal travel times and shifts in their carrier phase (phase advance). Fast and reliable positioning requires a good model of the spatio-temporal correlations of the ionosphere to correct for these non-geometric influences.
Network solutions using multiple reference stations of known location allow correction terms to be extracted from the signal measurements; those corrections can be interpolated to all locations within the network. See for example U.S. Pat. No. 5,477,458 “Network for Carrier Phase Differential GPS Corrections” and U.S. Pat. No. 5,899,957 “Carrier Phase Differential GPS Corrections Network.”
FIG. 2 illustrates a network technique in which N ground-based reference stations of known location 211, 212, 213, 21N receive GNSS signals from M satellites 221, 222, . . . , 22M. The GNSS signals are perturbed by the ionosphere 230, by the troposphere and by multipath effects. The coordinates of each reference station are known precisely. These stations use GNSS signal measurements of the current epoch and their known location to calculate a residual error with respect to each satellite m. In this way each reference station n obtains a pseudorange correction (PRC(t; t0; n; m)) for each observed satellite m. These corrections are transmitted to a central station 240 which lies within or outside of the network. Central station 240 calculates pseudorange corrections for a location close to the rover's last position and sends these to the rover. The rover can use the pseudorange corrections to improve its current position estimate.
In this network technique, all of the errors used in the position estimates are lumped together as a residual, disregarding their individual characters, such as short range correlations in multipath and long range correlations in the ionosphere. Calculating pseudorange corrections is done by interpolating residual errors of the reference stations.
There have been attempts to extract two- or even three-dimensional information on the ionosphere from GPS measurements. See S. M. RADICELLA et al., A Flexible 3D Ionospheric Model for Satellite Navigation Applications, PROCEEDINGS GNSS 2003, Japan; and F. AZPILICUETA et al., Optimized NeQuick Ionospheric Model for Point Positioning, PROCEEDINGS GNSS 2003, Japan. In the Nequick 3D model, the vertical structure of the ionosphere is parameterized in terms of profiling functions that capture the main characteristics of the ionospheric layer.
Also known are ‘tomographic’ models which break the ionosphere into a 3-dimensional grid that surrounds the earth. See O. L. COLOMBO et al., Resolving Carrier-Phase Ambiguities on the Fly, at more than 100 km from nearest Reference Site, with the Help of Ionospheric Tomography, ION GPS 1999, Nashville; M. HERNANDEZ-PAJARES et al., New Approaches in Global Ionospheric Determination using Ground GPS Data, JOURNAL OF ATMOSPHERIC AND SOLAR-TERRESTRIAL PHYSICS (61) 1999, 1237; M. HERNANDEZ-PAJARES et al., Application of Ionospheric Tomography to Real-Time GPS Carrier-Phase Ambiguities Resolution, at Scales of 400-1000 km and with High Geomagnetic Activity, GEOPHYSICAL RESEARCH LETTERS, 13 (27) 2000, 2009; M. HERNANDEZ-PAJARES et al., Precise Ionospheric Determination and its Application to Real-Time GPS Ambiguity Resolution, ION GPS 1999, Nashville. Due to limited data and computing power, such an ionospheric grid must remain rather coarse.
Other modeling efforts combine the ionospheric measurements across the hemisphere visible to a satellite and apply a spherical expansion for the entire hemisphere. See Y. LIU et al., Development and Evaluation of a New 3-D Ionospheric Modeling Method, NAVIGATION 4 (51) 2004, 311. In this work, the altitude dependence is modeled by a linear combination of orthogonal functions. The authors of this approach hope to extract a correlation in the ionosphere across distances of thousands of kilometers.
Without assuming any correlation between the stations, Hansen et al. trace the electron content along the signal path through the ionosphere. See A. J. HANSEN et al., Ionospheric Correction Using Tomography, ION GPS 1997, Kansas City; and D. BILITZA, International Reference Ionosphere 2000, RADIO SCIENCE 2 (36) 2001, 261.
There have also been studies on the interpolation of the ionospheric residual to the approximate location of a rover within a network of known stations. See D. ODIJK, Improving Ambiguity Resolution by Applying Ionosphere Corrections from a Permanent GPS Array, EARTH PLANETS SPACE 10 (52) 2000, 675; D. ODIJK, Weighting Ionospheric Corrections to Improve Fast GPS Positioning Over Medium Distances, ION GPS 2000, Salt Lake City; and D. ODIJK, Fast Precise GPS Positioning in the Presence of Ionospheric Delays, Ph.D thesis, Dept. of Mathematical Geodesy and Positioning, Delft University of Technology, Delft University Press, The Netherlands, 2002. These models typically introduce one ionospheric parameter for each station-satellite combination, which is estimated for each station independently. These independent observations are interpolated to the approximated rover location to offer a correction value to the user.
Techniques have also been proposed for ionospheric modeling and integer ambiguity resolution with the larger number of frequencies that will be supplied by modernized GPS and GALILEO. See T. RICHERT et al., Ionospheric Modeling, GPS WORLD, June 2005, 35.